Related papers: A systematic approach to computing and indexing th…
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…
In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…
We present a unified constructive digit-by-digit framework for exact root extraction using only integer arithmetic. The core contribution is a complete correctness theory for the fractional square root algorithm, proving that each computed…
The Carrell-Chapuy recurrence formulas dramatically improve the efficiency of counting orientable rooted maps by genus, either by number of edges alone or by number of edges and vertices. This paper presents an implementation of these…
A targeted exponentiation algorithm computes a group exponentiation operation $a^k$ with a reversible circuit in such a way that the initial state of the circuit consists of only the base $a$ and fixed values, and the final state consists…
Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions…
For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
Computing the roots of a univariate polynomial is a fundamental and long-studied problem of computational algebra with applications in mathematics, engineering, computer science, and the natural sciences. For isolating as well as for…
In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is…
This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in…
The algorithms of Pan (1995) and(2002) approximate the roots of a complex univariate polynomial in nearly optimal arithmetic and Boolean time but require precision of computing that exceeds the degree of the polynomial. This causes…
$\beta(1,0)$-trees provide a convenient description of rooted non-separable planar maps. The involution $h$ on $\beta(1,0)$-trees was introduced to prove a complicated equidistribution result on a class of pattern-avoiding permutations. In…
Zernike radial polynomials (ZRP) play a significant role in application areas such as optics design, imaging systems, and image processing systems. Currently, there are two kinds of numerical schemes for computing the ZRP automatically with…
Using the interplay between topological, combinatorial, and geometric properties of polynomials and analytic results (primarily the covering structure and distortion estimates), we analyze a path-lifting method for finding approximate…
A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function $U(a,z)$ in domains of the complex plane is presented. The algorithm uses accurate approximations to the first zero plus a highly…
Modern programmable digital signal processing relies on floating-point numbers for their ease of use. Fixed-point number formats have the potential to save resources and improve execution time, but realising this potential burdens the…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
In this paper we investigate iterative roots of strictly monotone upper semi-continuous multifunctions having finitely many jumps. Known results are concerning roots of order 2 for multifunctions of exact one jump. For the general…
For enumerative problems, i.e. computable functions f from N to Z, we define the notion of an effective (or closed) formula. It is an algorithm computing f(n) in the number of steps that is polynomial in the combined size of the input n and…